Partitions and ordered products

Abstract: Let $g(n)$ be the number of ways to express $n$ as an ordered partition of numbers greater than $1$. We also let $a(n)$ be the number of partitions of $n$ of the form $n_1 + n_2 + \cdots + n_k$, where $n_i$ is a multiple of $n_{i + 1}$ and the $n_i$ are distinct. Though there is substantial research around $g(n)$, much less is known about $a(n)$. We discuss these two functions, as well as some new asymptotics on $a(n)$.

Mathematics

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2025)